I'm writing this comment in English. My native language is different and the vast majority of spoken interactions in my private life isn't in English. English isn't even an official language in my country.
Your argument is crass, but I think you're being needlessly romantic. Unlike skin colour, you can "wear" more than one language and switch between them as appropriate.
In fact, if you spend any time studying linguistics you will quickly learn that even "monolingual" speakers speak different languages depending on the context. We classify these as different registers or sociolects but ultimately the effect is the same:
The language we speak heavily depends on who we are speaking to, not only on who we are.
Whether we can preserve languages that are effectively running out of contexts to be useful in is another question. But that is basically an argument about controlling natural evolution. And that's actually a solved problem: just look at how we preserve other cultural artefacts like art and crafts.
Also, just because a culture is disappearing doesn't mean no new cultures will be created. I'm sure the Romans never worried about their language going away yet the modern "lingua franca" is ultimately a descendent of a bunch of regional varieties of a language closely related to Old Norse. A thousand years from now the worry about the future of AAVE will seem as quaint as the worry about the future of Kentish Old English would seem now (if anyone worried at the time at all).
Heck, the situation of AAVE is actually infinitely better than that of Kentish Old English: there is a wealth of contemporary study into AAVE and thanks to modern technology it is trivial to archive speech samples, even including the spoken word and interviews with native speakers.
If you ignore the politicisation of this issue (because all "race" issues are political in the US, even when they're supposedly about language) the decline of AAVE is no more tragic than the decline of any other regional or social language.
Preserving languages is a solved problem. There is no reason to worry about AAVE beyond ensuring its preservation except for race politics.